Question

Simplify:

(i) $\frac{173\times 173\times 173+127\times 127\times 127}{173\times 173-173\times 127+127\times 127}$

(ii) $\frac{155\times 155\times 155-55\times 55\times 55}{155\times 155+155\times 55+55\times 55}$

(iii) $\frac{1.2\times 1.2\times 1.2-0.2\times 0.2\times 0.2}{1.2\times 1.2+1.2\times 0.2+0.2\times 0.2}$

Answer 1

(i) The given expression is

Assumeand. Then the given expression can be rewritten as

Recall the formula for sum of two cubes

Using the above formula, the expression becomes

Note that both and b are positive. So, neithernor any factor of it can be zero.

Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes

(ii) The given expression is

Assumeand. Then the given expression can be rewritten as

Recall the formula for difference of two cubes

Using the above formula, the expression becomes

Note that both, b is positive and unequal. So, neithernor any factor of it can be zero.

Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes

(iii) The given expression is

Assumeand. Then the given expression can be rewritten as

Recall the formula for difference of two cubes

Using the above formula, the expression becomes

Note that both, b is positive and unequal. So, neithernor any factor of it can be zero.

Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes